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Chemical Engineering Thermodynamics-I Lecture 4

Chemical Engineering Thermodynamics-I Lecture 4. Prof.Dr.Mahmood Saleem Institute of Chemical Engineering & Technology University of the Punjab, Lahore. Contents. Introduction Property relations for Homogeneous Phase Residual Properties Residual Properties by Equation of State

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Chemical Engineering Thermodynamics-I Lecture 4

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  1. Chemical Engineering Thermodynamics-ILecture 4 Prof.Dr.Mahmood Saleem Institute of Chemical Engineering & Technology University of the Punjab, Lahore

  2. Contents • Introduction • Property relations for Homogeneous Phase • Residual Properties • Residual Properties by Equation of State • Property Relations for Two Phase Systems • Thermodynamic Property Diagrams and Tables • Generalized property Correlations for Gases • Extension of Generalized property Correlations for Gases to Mixtures • Exercises

  3. Introduction • Processing of materials (pure and mixtures) is key affair in chemical processes • Estimation of many properties (and change) other than volumetric properties (H,U,s,G etc.) are required. • How to know complete property set when volumetric properties are not available • What tools can one use to handle such issues?

  4. Property Relations for Homogeneous PhasesFundamental Properties • Although equation (6.1) is derived from the special case of a reversible process, it not restricted in application to reversible process. • It applies to any process in a system of constant mass that results in a differential change from one equilibrium state to another. • The system may consist of a single phase or several phases; may be chemically inert or may undergo chemical reaction. …(6.1)

  5. Definitions H = Enthalpy A = Helmholtz energy G = Gibbs energy …(2.11) …(6.2) …(6.3)

  6. Based on one mole (or to a unit mass) of a homogeneous fluid of constant composition, they simplified to • Function Change

  7. Maxwell’s equations

  8. Enthalpy and Entropy as Functions of T and P • Temperature derivatives: • Pressure derivatives:

  9. The most useful property relations for the enthalpy and entropy of a homogeneous phase result when these properties are expressed as functions of T and P (how H and S vary with T and P). …(6.20) …(6.21)

  10. Property Relations for Homogeneous PhasesInternal Energy as Function of P (U(P)) • The pressure dependence of the internal energy is shown as

  11. Property Relations for Homogeneous PhasesThe Ideal Gas State • For ideal gas, expressions of dH and dS (eq.6.20-6.21) as functions of T and P can be simplified as follows using ideal gas law:

  12. Property Relations for Homogeneous PhasesAlternative Forms for Liquids • Relations of liquids can be expressed in terms of  and  as follows:

  13. Property Relations for Homogeneous PhasesAlternative Forms for Liquids • Enthalpy and entropy as functions of T and P as follows: •  and  are weak functions of pressure for liquids, they are usually assumed constant at appropriate average values for integration.

  14. Practice 1 Determine the enthalpy and entropy changes of liquid water for a change of stage from 1 bar 25C to 1,000 bar 50C.

  15. Constant P Constant T

  16. Integrated forms of equations for change in Enthalpy and Entropy Average value at T1 and T2 at 1 bar Average value at P1 and P2 at 50 oC

  17. On substitution of values Note that the effect of P of almost 1,000 bar on H and S of liquid water is less than that of T of only 25C.

  18. Property Relations for Homogeneous PhasesInternal Energy and Entropy as Function of T and V • Useful property relations for T and V as independent variables are

  19. The Partial derivatives dU and ds of homogeneous fluids of constant composition to temperature and volume are • Alternative forms of the above equations are

  20. Property Relations for Homogeneous PhasesThe Gibbs Energy • An alternative form of a fundamental property relation as defined in dimensionless terms: • The Gibbs energy when given as a function of T and P therefore serves as a generating function for the other thermodynamic properties, and implicitly represents complete information.

  21. Residual Properties • The definition for the generic residual property is: Mig = the ideal gas properties which are at the same temperature and pressure. M = the Residual Molar gas properties which are at the same temperature and pressure. M is the actual molar value of any extensive thermodynamics property: V, U, H, S, G.

  22. Residual Gibbs energy: • Residual volume: PV=ZRT

  23. Fundamental property relation for residual properties • The fundamental property relation for residual properties applies to fluids of constant composition.

  24. Enthalpy and Entropy from Residual Properties

  25. The true worth of the Eq. for ideal gases is now evident. They are important because they provide a convenient base for the calculation of real-gas properties.

  26. Practice 2 Calculate H and S of saturated isobutane vapor at 630 K from the following information: • Table 6.1 gives compressibility-factor data • The vapor pressure of isobutane at 630 K 15.46 bar • Set H0ig = 18,115 Jmol-1 and S0ig = 295.976 Jmol-1K-1 for the ideal-gas reference state at 300 K 1 bar • Cpig/R = 1.7765+33.037x10-3T (T/K)

  27. Solution 6.3 • Eqs. (6.46) and (6.48) are used to calculate HR and SR. • Plot (Z/T)P/P and (Z-1)/P vs. P • From the compressibility-factor data at 360 K  (Z-1)/P • The slope of a plot of Z vs. T  (Z/T)P/P • Data for the required plots are shown in Table 6.2.

  28. Residual Properties by Equations of StateResidual Properties from the Virial Equation of State • The two-term virial eq. gives Z-1 = BP/RT.

  29. In application  is a more convenient variable than V, PV = ZRT is written in the alternative form.

  30. The three-term virial equation. Application of these equations, useful for gases up to moderate pressure, requires data for both the second and third virial coefficients.

  31. Residual Properties by Cubic Equations of State

  32. The generic equation of state presents two cases.

  33. Ex. 6.4 Find values for the HRand SR for n-butane gas at 500 K 50 bar as given by the Redlich/Kwong Eequation. Solution Tr = 500/425.1 = 1.176, Pr = 50/37.96 = 1.317 From Table 3.1:

  34. These results are compared with those of other calculation in Table 6.3.

  35. TWO-PHASE SYSTEMS The Clapeyron eq. for pure-species vaporization

  36. Temperature Dependence of the Vapor Pressure of Liquids

  37. Corresponding-States Correlations for Vapor Pressure The reduced normal boiling point The reduced vapor pressure corresponding to 1 atm

  38. Ex. 6.6 Determine the vapor pressure for liquid n-hexane at 0, 30, 60 and 90C: (a) With constants from App. B.2. (b) From the Lee/Kesler correlation for Prsat Solution (a) (b) Eq.(6.78); From Table B.1, From Eq.(6.81)   =0.298 The average difference from the Antoine values is about 1.5%.

  39. Two-Phase Liquid/Vapor System

  40. THERMODYNAMIC DIAGRAMS

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